# Semantic search

AEP upper-hook characteristic implies AEP, Additive group of a field implies characteristic in holomorph, Analogue of critical subgroup theorem for finite solvable groups, Center is characteristic, Centerless and characteristic in automorphism group implies automorphism group is complete, Characteristic and self-centralizing implies coprime automorphism-faithful, Characteristic central factor of WNSCDIN implies WNSCDIN, Characteristic equals fully invariant in odd-order abelian group, Characteristic equals strictly characteristic in Hopfian, Characteristic equals verbal in free abelian group, Characteristic implies automorph-conjugate, Characteristic implies normal, Characteristic maximal subgroups may be isomorphic and distinct in group of prime power order, Characteristic not implies amalgam-characteristic, Characteristic not implies characteristic-isomorph-free in finite, Characteristic not implies direct factor, Characteristic not implies elementarily characteristic, Characteristic not implies fully invariant, Characteristic not implies fully invariant in class three maximal class p-group, Characteristic not implies fully invariant in finite abelian group, Characteristic not implies fully invariant in finitely generated abelian group, Characteristic not implies fully invariant in odd-order class two p-group, Characteristic not implies injective endomorphism-invariant, Characteristic not implies injective endomorphism-invariant in finitely generated abelian group, Characteristic not implies isomorph-free in finite group, Characteristic not implies isomorph-normal in finite group, Characteristic not implies normal-isomorph-free, Characteristic not implies potentially fully invariant, Characteristic not implies powering-invariant in solvable group, Characteristic not implies quasiautomorphism-invariant, Characteristic not implies strictly characteristic, Characteristic not implies sub-(isomorph-normal characteristic) in finite, Characteristic not implies sub-isomorph-free in finite group, Characteristic of CDIN implies CDIN, Characteristic of normal implies normal, Characteristic of potentially characteristic implies potentially characteristic, Characteristic subgroup of Sylow subgroup is weakly closed iff it is normal in every Sylow subgroup containing it, Characteristic subgroup of abelian group not implies divisibility-closed, Characteristic subgroup of abelian group not implies local powering-invariant, Characteristic subgroup of additive group of odd-order Lie ring is derivation-invariant and fully invariant, Characteristic subgroup of uniquely p-divisible abelian group is uniquely p-divisible, Characteristic subset generates characteristic subgroup, Characteristic upper-hook AEP implies characteristic, Characteristicity does not satisfy image condition, Characteristicity does not satisfy intermediate subgroup condition, Characteristicity does not satisfy lower central series condition, Characteristicity is centralizer-closed, Characteristicity is commutator-closed, Characteristicity is not finite direct power-closed, Characteristicity is not finite-relative-intersection-closed